List of Tables
Chapter 2 Joining of a tube to a sheet through end curling
2.2 Results and discussion
2.2.9 FE simulation of pull-out tests of end formed joint .1 Variation in „D‟ for different cases
Chapter 2 welded structure is quite high as compared to flat die and die with inclination of 10º. As a
result, energy absorbed increases for welded structure.
2.2.9 FE simulation of pull-out tests of end formed joint
Chapter 2 and curled region) is elongated in vertical direction. Neck slightly expands and after that
rest of the deformation is concentrated in the curled region. „D‟ decreases up to a displacement about 12 mm. At this displacement the deforming end of the tube, which is initially horizontal due to designed geometry of the die becomes vertical and points in upward direction (Fig. 2.39). After this, deformation stops in the curled region of tube. As a result, „D‟ is maintained constant thereafter and with upward movement of tube, this vertical edge of tube pushes the bent sheet in the upward direction and sheet finally comes out of the curled part. During simulation studies complete unlocking is defined where the sheet finally comes out of the curled part of the tube. Inset images show the tube-sheet assembly at different stages of deformation for Case 1 during pull-out test simulation.
2.2.9.2 Validation of pull-out load-displacement results
Fig. 2.38 shows a comparison of load evolution between experimental and simulation trials. The nature of load evolution is slightly different for experimental and simulation trials. In case of experimental trials, load increases monotonically up to the displacement where complete unlocking takes place and after that load suddenly decreases. In case of simulation, peak load is attained either at the start of the process or at some intermediate displacement between start and end. For example, in the case of Case 1, peak load is attained at a displacement of 2.5 mm (Fig. 2.38a), while in case of Case 2 and 3 peak load is attained at a displacement of 8 mm ((Fig. 2.38(b, c)) under different testing conditions. Initial unlocking of tube from sheet needs larger load and once the joint becomes loose, load decreases monotonically up to the final unlocking displacement during simulation.
In case of experiments, though tube has been firmly bolted with punch, some slipping has been observed at the interaction of bolt and tube, while during simulation no slip condition has been defined between punch and tube surface. It can cause some deviation of load from the expected value during experiments. In experiments clamping has been done manually, which leads to different blank holding force. A difference in peak load between experimental and simulation trials have been observed. An average peak load difference „∆F (peal load)‟ for any case under different testing conditions has been calculated between experiments and simulations.
Chapter 2
Fig. 2.38 Load-displacement curves for (a) Case 1, (b) Case 2, and (c) Case 3 of end formed joints during FE simulations and experiments (S: Simulation, E: Experiment)
ΔF (peak load) has been observed as 34 kN, 25 kN and 28kN in case of Case 1, 2 and 3 respectively. The difference is minimum in Case 2, while it is maximum in Case 1.
Manual clamping, slip at the bolt-tube interface and modeling conditions attribute to such load difference. Load evolution during simulation for die inclination 10º and 15º is almost same for different cases and testing conditions, while a minor difference in load evolution is observed for flat die as compared to angular dies. Peak load experienced for different testing conditions do not follow any trend for different cases during simulation. For example, in case of Case 1 maximum load is observed for die inclination of 15º, in case of Case 2 maximum load is observed for die inclination of 15º, and in case of Case 3 maximum load is observed for flat die. During experiments, maximum load is experienced by flat die for different cases under different testing conditions, while during simulation for Case 1 and 2 same trend is not followed. Flat die takes lesser displacement
Chapter 2 to completely unlock as compared to angular dies for different cases and testing
conditions which is in agreement with experimental result.
Load evolution curve during simulation also conveys the quality of compactness of the joint. For example, for all cases and testing conditions, the load experienced by Case 1 under flat die and die inclination of 15º is largest. Also the displacement at which it is observed is minimum as compared to other cases. It means the most compact joint is obtained in case of Case 1.
Fig. 2.39 shows the completely unlocked images (sectioned view) of tube-sheet end formed joints during pull-out tests. Deformation behaviour of tube and sheet for different cases on different die inclination is clearly visible. The height between neck and curled part of tube for Case 3 (Fig. 2.39 (g-i)) is larger as compared to other cases.
Fig. 2.39 Sectioned and completely unlocked images (tube-sheet) for different cases at different testing conditions
von-Mises stress contour in the tube and the sheet is also different on angular dies as compared to flat dies. The equivalent stress generated in the supported region of tube
Chapter 2 in flat dies is almost negligible, but on angular dies, the stresses are generated in the
supported region of tube. It means that on flat dies, the whole deformation is concentrated in the joint region, while similar situation does not exist for angular dies.